A novel development of a new single switch inductor coupled DC-DC converter for PV system with two-leg inverter

From the power generation history, the nonrenewable power sources utilization is falling extremely because of their demerits are high atmospheric pollution, more expensive, more catchment area for development, high fossil fuel transportation cost, less flexibility, and reliability. So, the sunlight systems are utilized in this work for feeding the power to the central grid. On the earth, the sunlight energy availability is more and it is more flexible for the installation. However, the sunlight photovoltaic (PV) module’s power production is very low. To improve the power generation of the PV network, a modified slider maximum power point tracking (MPPT) controller is proposed in the first objective and it is interfaced with the sunlight system for capturing more sunlight insolation thereby moving the functioning point of the solar system from local MPP place to required global MPP place. The features of this sliding controller are continuous peak power production, easy development, less power dissipation losses, plus good dynamic system response. In the second objective, the available voltage of the PV is low which improved from low level to high level by utilizing the Wide voltage supply-inductor coupled converter. The development of this circuit needed very less inductive, plus capacitive components. Also, it is developed by selecting a single switch. As a result, the entire network power production cost is reduced. In the third objective, a two-leg inverter is proposed for the transformation of the DC voltage supply into three-phase powers. The MATLAB/Simulink tool is used to investigate the overall system.

by integrating the incremental conductance method.This controller takes a slightly higher implementation cost when associated with the P&O concept.The limitations of both usual methods are compensated by choosing the lookup table power point identifier 18 .This method takes very low voltage rating components, plus easy handling at quick variations of sunlight conditions.However, these methods are not suitable for the shaded conditions of the sunlight network.
The artificial intelligence concept is illustrated in the article 19 for balancing the voltage of the battery-interfaced wind energy network to supply uniform power to the automotive industry.The artificial controller's development has been done by utilizing the working principle human brain.Here, each neuron is identified as one node and all the neurons are interfaced with the help of dendrites.The neurons collect the information from previously existing neurons for identifying the optimal solution for the nonlinear performance-based sunlight system.In the article 20 , the authors focused on the P&O with artificial intelligence MPPT controller for capturing the exact place of the microgrid-based wind/solar power production network.This hybrid algorithm development cost is low and reduces distortions across the functioning point of the sunlight network.Also, the flexibility, plus reliability of the overall wind/solar system are more by using this power point tracking controller.However, these controllers suffer from more power losses of the sunlight system under shading behavior conditions.
So, the adaptive modified slider MPPT methodology is developed in this article for running the overall system at peak power point conditions.The advantages of this proposed method when associated with the conventional controllers are easy operation, less complexity in understanding, low passive components necessary for developing the controller, and more suitability for the uniform and continuous changes of sunlight irradiation conditions.The available voltage of the inductors linked DC-DC converter is sent to the two-leg bridge converter for transferring the DC source into the AC source for supplying the energy to the local consumers, plus the utility grid.The remaining part of the work is organized as in Sect."Modeling of proposed PV system and its description", the mathematical development of the sunlight system cell, and its overall system description is mentioned.From Sect."Proposed universal source voltage converter for PV", the proposed converter voltage conversion ratio is obtained by adjusting the coupled inductor turns, and its power point identification by using modified MPPT methodology is mentioned in detail in Sect."Small signal analysis of proposed slider controller".The development of the introduced two-leg bridge inverter is discussed in Sect."Development of power inverter circuit for solar PV".Finally, the proposed sunlight network and its functioning strategy are explained in Sect."Discussion of simulation results".The conclusion of the proposed controller is given in Sect."Conclusion".

Modeling of proposed PV system and its description
The sunlight network's operating efficiency depends on its accurate nonlinear characteristics 21 .The one diode network development has been done based on the five constraints which are parallel resistance (R Pt ), openly circuited PV network voltage (V OcV ), ideality factor (β n ), serially placed resistance (R Sy ), plus PV output short-circuited current (I Sci-n ).The merits of one diode network are a very simple structure, less iteration number required for identifying the optimal parameters of the sunlight system, less development cost, plus simple understanding.However, it may not generate pure I-V Characteristics of the sunlight network because its junction recombination operation effect is neglected.So, a dual diode concept is applied in the PV-integrated electric vehicle charging station to enhance the power production ability of the PV system.This model needed a few more variables because one more power semiconductor device is involved in the one diode circuit-based sunlight system which is diode reverse back current (I Sci-m ), plus its related ideality parameter (β m ).Here, all the junction's reverse leakage currents are removed by involving one more diode in the dual diode-based sunlight network.
Here, the proposed 3-diode configuration circuit needs overall nine constraints which are parallel resistance (R Pt ), openly circuited PV network voltage (V OcV ), ideality factors (β n , β m , plus β b ), serially placed resistance (R Sy ), plus PV output reverse short-circuited currents (I Sci-n , I Sci-m , plus I Sci-b ).All the variables are properly identified by utilizing the various nature-inspired algorithms.From the literature study, the parameter's identified algorithms are Jaya, Differential Evolutionary, wind drive optimization, plus soft computing methodologies.In this work, the 3-diode sunlight network parameters are obtained by applying the modified cuckoo search concept which is illustrated in Table 1.From Fig. 3), plus Fig. 3b, in the 1st circuit, the shunt resistive element is not taken into account because the reverse leakage current value is much less.However, in practical circuit working conditions, the shunt resistance comes in the sunlight system.So, the sunlight system generated current is represented as I Pw and it is evaluated by selecting Eq. (1).The obtained V-I & P-V curves of the sunlight network are illustrated in Fig. 4a, and b. (1)

Proposed universal source voltage converter for PV
The PV power network energy production required more higher installation cost.To limit this issue, there are various power converter network topologies are interlinked with the solar system for the production of peak voltages for the local load consumers 22 .As we know the isolated circuit topologies needed more passive components, and its manufacturing cost is also more.Here, the two inductors interlinked concept is utilized for moderate, plus more power automotive applications.This converter voltage conversion ratio is enhanced by the continuous adjustment of the transformer's two windings turns which are represented as N Pr , plus N Se .The turns ratio of the proposed converter is N ti which is decided based on the secondary windings of transformer turns with associated the source winding turns.The working network of the proposed converter is illustrated in Fig. 5. From Fig. 5, the Insulated Gate Bipolar Transistor (IGBT) power semiconductor switch (Q) is selected for the development of the power converter circuit.The features of this switch are high source voltage control ability, high source

+ -
Proposed wide voltage conversion ratio power converter circuit.
impedance, low driver circuit cost, easy-to-make parallel operation, plus the ability to function above 200 °C temperature.Also, this switch's starting functioning speed is very high when associated with the other controllers.
Here, the sunlight source is directly sent to the converter network to improve the fill factor of the overall system.The dotted circle near the source inductor (L s ), plus the resistor (R s ) is defined as the current in flow.The currents, plus their related voltages flowing to the parameters L s , plus L 0 are I Ls , I L0 , V Ls , plus V L0 .Similarly, for the variables (L s , plus L 0 ) currents and voltages are I Rs , I R0 , V Rs , plus V R0 .The coupled capacitors parameters are identified as C ldc-1 , plus C ldc-2 , and their associated voltages and currents flowing through these elements are I ldc-1 , I ldc-2 , V ldc-1 , plus V ldc-2 .These DC-linked source voltages are interlined with the inverter input.The voltage conversion of the converter network is illustrated in Eq. ( 8).From Eq. ( 8), plus Eq. ( 10), the terminologies N tura , plus R total are the overall inductors turns ratio and its related total resistance.The design constraints of the introduced converter circuit are discussed in Table 2.

Small signal analysis of proposed slider controller
In most of the existing power converter networks, there are more than two sensors are required.For all these sensing variables, the evaluation of state constraints is mandatory for identifying the duty pulses to the introduced coupled inductor converter network.In this proposed controller network, the error constants are enough for the effective operation of the converter network.From Fig. 6, the low-pass filter circuited is applied for transferring the direct current values to sinusoidal signals.Here, the low-pass network optimizes the entire sunlight system size.As a result, the cost, plus the required components for the development of the controller circuit is low.Also, this controller handles the nonlinear nature of the sunlight system very effectively thereby the converter circuit supplies wide supply voltage gain with low-level duty values.This controller tries to maintain uniform DC-link voltages at static irradiation as well as rapid variation of sunlight temperatures.In this section, the step-by-step process of the converter network development is discussed.Here, the straightforward inductor flux measurement is a quite tough task.So, the state constraints of inductors (I x ) are used to determine the flux linkages of the inductors.
Table 2. Design constraints of introduced DC-DC converter circuit for sunlight system.www.nature.com/scientificreports/

S. no Names of variables
Here, the condition of the first state variable § ∈ {0, 1} then the switching condition of the converter is men- tioned in Eq. ( 17).The error variable state vector is illustrated in Eq. ( 18).The overall mathematical term of the converter is given in Eq. ( 19).
From Eqs. (17) to (22), the modified structure concept is applied to the slider controller for identifying the sunlight structure slider regions.The slider region S(f) values should be in the bounded condition.So, the overall structure works in variable sunlight insolation conditions as mentioned in Eq. ( 23).The sliding regions require state trajectories which are evaluated from the surface conditions.For evaluating the converter states which are ( 14) closely near to the slider surface then the controller operation is given in Eq. ( 25).From Eqs. ( 22) to (25), the overall controller working conditions are mentioned in Eq. ( 26).The design variables of the controller are mentioned in Table 3, and the working of the adaptive modified slider controller is mentioned in Fig. 6.From Fig. 6, the converter network produces more distortions which are utilized in this network for running the sunlight MPP position at the actual MPP place.In this controller, the integrator, plus the filter network are combined to suppress the fluctuations of sunlight power.The high noise frequency values are eliminated by applying the gradient (Δ) value.From the controller structure, the error signal is associated with the sine value for tracing the global MPP place.The parameter V re Peak is forwarded to the slider network for evaluating the converter duty values range.The selected signals to the sliding system are sunlight insolation, sunlight supply voltage, plus sunlight current.Here, with the continuous fluctuations of solar insolation, the slider maintains the constant MPP position.

Development of power inverter circuit for solar PV
The available supply of the converter circuit may not be fed directly to the grid network.So, the power transformation has been made by selecting the DC-AC conversion circuit.In the article 23 , the authors discussed the 3-leg bridge circuit for obtaining the three-phase power which is interlinked with the household, and gird power networks.However, this type of 3-leg circuit is not flexible for the uniform power supply to the central grid network because if any one of the switches fails, the entire power production network fails 24 .As a result, the overall network heating losses, plus harmonics losses are In this proposed grid network, a 2-leg topology is introduced to eliminate the discontinuity in the grid supply power which is shown in Fig. 7. From Fig. 7, the first leg of the inverter circuit is interlinked with the phase (m), and the 2nd leg of the circuit is interfaced with the grid phase (o).Finally, the middle phase of the grid network is connected to the neural point of the DC-AC circuit which is named 'n' .The design constraints of this circuit are mentioned in Tables 2 and 3, and its functioning Table 3. Design values of adaptive modified slider controller structure.

2.
The integrator of the slider controller utilized gain (K c ) 6.2719

4.
The surface constraint of the slider at horizontal condition (£ 1 ) 4.4431
The entire system functioning frequency at diverse Sunlight systems (ω) 99.982 rad/sec 7.
The entire system higher cutoff functioning frequency ( ω h ) 9.9879 rad/sec www.nature.com/scientificreports/pulses are illustrated in Fig. 8. From Fig. 8, the devices T m , plus 1-T n start functioning at a time to supply the voltage V Inv_M .Also, the devices T n , plus 1-T m work in the opposite way when associated with the previous state of operation.The voltages V P-M , plus V P-N are appeared between the transmission lines 'M' , and 'N' , and its RMS value is 'e' .The circuit L n -C n helps eliminate the 3rd-order harmonics at non-uniform insolation values.

T-4 switching pulses generation by using slider technology
From Fig. 7, the T-4 circuit starts functioning by interconnecting the slider block.The slider circuit receives all the inverter circuit state variables which are defined as m cn , ∅ 1 , ∅ 2 , ∅ 3 , ∅ 4 plus V DC-1,2 .Here, the DC-link circuit voltages are helpful for equal power distribution to the grid network.The supply side inverter circuit voltage voltage is identified by comparing it with the reference voltage V ref .
The inverter supply error voltage is applied to the slider block to suppress the fluctuations of dc-link voltages thereby the grid tries to work at the accepted power factor of the load.The LPF network helps the grid circuit maintain the uniform RMS voltages with a unity power factor.The term "ε" is adjusted continuously for supplying the balanced power to the local consumers.The mathematical representation of the inverter circuit, angle of displacement, plus overall grid angle of impedance is derived in Eq. ( 30).The functioning states of the DC-AC circuit are discussed in Table 4. (

Discussion of simulation results
The sunlight network is developed by considering the 3-diode solar system because its features are more efficient, highly accurate power, and current characteristics.Also, this circuit fill factor is little high when associated with the 1-diode, plus 2-diode topologies.The design constraints of the sunlight network are mentioned in Table 1.The parameter C x helps maintain the uniform solar voltages irrespective of the sunlight insolation and its equivalent value is 10mF.The converter interlinked inductors support the solar system for enhancing the voltage profile of the PV array, and their design variables are defined in Table 2. Here, the utilized sunlight captured insolation values are 1000, 750, plus 500W/m 2 .
At uniform sunlight insolation, the extracted sunlight system power, solar voltage, plus PV currents are 96.82.99 kW, 0.4150 kV, and 0.02311kA respectively.The availed sunlight power at rapid variations environmental insolation is explained in Fig. 9. From Fig. 9, when the irradiations fall from uniform to 750W/m 2 then the stabilizing time is 0.42 s.Also, the power gets reduced from 96.82.99 to 6.8289 kW.In addition, the voltage at this irradiation value is 405.89V, plus the current supplied by the PV network is 16.18A.Finally, the availed sunlight network voltage at 0.5 kW/m 2 is 401.98 V, and its related solar system current, plus PV is 11.897A, plus 4.782 kW.
From Fig. 10, the utilized reference voltage is 1200 V which is associated with the actual available voltage of the converter output signal.Here, the inverter circuit output linked capacitors collect the sunlight voltage with equal load distribution.Here, both the capacitors' C ldc-1 , plus C ldc-2 voltages are equal to 599.891 V at quick changes of sunlight values which indicates that the neutral point of the proposed inverter circuit is constant, and balance the dc-link voltages of the capacitors.The balancing of neutral points helps the overall inverter network from the quick variation of PV network voltages.Also, the power of semiconductor devices damage possibility is reduced.So, the overall network functioning cost is optimized with the help of slider methodology.Here, the slider receives the sunlight voltages, and solar currents for producing the suitable duty value for the interlinked inductor converter circuit.The stabilizing of the converter circuit voltage is 0.035 s which is an acceptable value for all sunlight temperature conditions.The evaluated modified slider power point tracking controller efficiency is 95.6% at variable sunlight values.
The distortions content involved in the converter voltage is 2 V. From Fig. 11, the voltage of the interlinked capacitor varies between 604.89 and 598.22 V, and it's almost the same.However, the inverter-fed grid network currents at 1 kW/m 2 are 18A, and its available current at 0.75 kW/m 2 is 14.78A.Finally, at 0.5 kW/m 2 , the grid network current is 9.759A respectively.At a functioning frequency of 50 Hz, the grid supplied total harmonic (30)  content is 1.26% which is very low and it is evaluated by the interlinking of the modified slider technique.The obtained 3-phase grid available currents under diverse atmospheric conditions are illustrated in Fig. 12.Finally, the per unit voltages are considered because of the easy analysis of the overall sunlight-fed grid network system as mentioned in Fig. 13.The maximum THD value of this grid currents and load voltages is 0.06%.So, the modified slider block is very useful for the B-4 converter circuit to produce electrical energy at the unity power factor.

Conclusion
The triple diode sunlight circuit is considered for the development of PV modules because of its more accurate nonlinear curves, most effective in operating efficiency, plus more power extraction.In the first objective, a new interlinked inductor DC-DC power network is developed to reduce the installation price of the sunlight system.These converter features are wide source voltage, more voltage conversion ratio value, low passive components utilization, less catchment area needed, plus more flexibility.the duty signal production for the converter, plus the operation of inverter circuits at shaded conditions of the sunlight system is a little challenging task.So, the modified slider methodology is introduced in the 2 nd objective for extracting more sunlight power and supplying the energy to the local networks and grids at unity power factor.The features of this proposed MPPT controller are fast MPP identification, low design complexity, easy operation, plus good understanding.Finally, in the third objective, the B-4 inverter circuit is proposed for uniform energy supply to the loads at all types of atmospheric conditions.

Figure 1 .
Figure 1.Overall, the steps involved power conversion system, (a) DC source, plus (b) AC source.

Figure 3 .
Photon current flow of sunlight network at multiple irradiations values (I Pc ) 24.390A Currents of utilized diodes under saturation conditions (I Sci-b , I Sci-m , I Sci-b ) 1.44 × 10 -10 amps Utilized sunlight insolation values for testing the proposed converter network (G) 1 k, 0.75 K, plus 0.5 KW/m 2 I on = I on_n = I on_m = I on_b = I Sci_n e Voc_n β * V * Tn .

Figure 4 .
Figure 4. (a) Available I-V characteristics of PV system.(b) Available P-V characteristics of PV system.

Figure 6 .
Figure 6.Solar power point tracker by using a modified slider controller.

Figure 8 .
Figure 8. Switches operating states at quick changes of sunlight values.

Figure 9 .
Figure 9. Extracted sunlight network power by utilizing the 3-diode solar PV circuit.

Figure 10 .
Figure 10.Converter network produced voltage signal at quick change of sunlight values.

Figure 13 .
Figure 13.Available per unit grid network current, plus inverter supplied voltages.

Table 1 .
Considered variables for the implementation of triple diode-dependent PV network.

Table 4 .
Switching operation of two-leg three-phase inverter.